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DOE OSTI2013

Saturation of multi-laser beams laser-plasma instabilities from stochastic ion heating

Cross-beam energy transfer (CBET) has been used as a tool on the National Ignition Facility (NIF) since the first energetics experiments in 2009 to control the energy deposition in ignition hohlraums and tune the implosion symmetry. As large amounts of power are transferred between laser beams at the entrance holes of NIF hohlraums, the presence of many overlapping beat waves can lead to stochastic ion heating in the regions where laser beams overlap [P. Michel et al., Phys. Rev. Lett. 109, 195004 (2012)]. This increases the ion acoustic velocity and modifies the ion acoustic waves’ dispersion relation, thus reducing the plasma response to the beat waves and the efficiency of CBET. This pushes the plasma oscillations driven by CBET in a regime where the phase velocities are much smaller than both the electron and ion thermal velocities. CBET gains are derived for this new regime and generalized to the case of multi ion species plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Intermittent fluctuations in the Alcator C-Mod scrape-off layer

Fluctuations in the boundary region of the Alcator C-Mod tokamak have been analyzed using gas puff imaging data. It is found that the fluctuation amplitudes in the near scrape-off layer follow a normal distribution while the far scrape-off layer fluctuations are dominated by large amplitude bursts due to radial motion of blob-like structures and have a positively skewed and flattened amplitude probability distribution. Conditional averaging of the time series reveals burst wave forms with a fast rise and slow decay and exponentially distributed burst amplitudes and waiting times. Based on this, a stochastic model of the burst dynamics is constructed. The model predicts that fluctuation amplitudes should follow a Gamma distribution and that there is a parabolic relation between the skewness and the kurtosis moments of the fluctuations. This is shown to compare favorably with the gas puff imaging data over a range of line-averaged plasma densities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Hot-electron generation from laser–pre-plasma interactions in cone-guided fast ignition

Two-dimensional particle-in-cell (PIC) simulations were performed for the cone-in-shell integrated fast-ignition experiments at the Omega Laser Facility [W. Theobald et al., Phys. Plasmas 18, 056305 (2011)]. The initial plasma density profile in the PIC simulations was taken from hydrodynamic simulations of the prepulse interaction with the gold cone. Hot-electron generation from laser–pre-plasma interactions and transport up to 100× the critical density (n c ) was studied. The simulation showed a mean divergence half-angle of 68° and 50% absorption for the hot electrons. The simulation results show that the generated hot electrons were dominated in number by low-energy electrons but in energy by multi-MeV electrons. Electron transport between 5 and 100 n c was ballistic. In the late stage of the simulation, all the results were largely independent of polarization, indicating a stochastic hot-electron–generation mechanism.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

3-D effects on viscosity and generation of toroidal and poloidal flows in LHD

Three-dimensional effects on plasma flows have been experimentally studied in the large helical device with 3D configurations. Spontaneous toroidal flow without net driving force using the combination of perpendicular neutral beam injection (NBI) heating and balanced tangential NBI heating has been investigated with two magnetic configurations. Co- and counter-directed spontaneous flows have been observed depending on the collisionality. Toroidal flow shear changes the sign at 0.4<r{sub eff}<0.6 between co- and counter-flowing plasmas, where r{sub eff} is a averaged minor radius. The detailed flow structures have been also examined at the edge region with stochastic magnetic field. A poloidal flow driven by the positive radial electric field has been observed at the open field region just outside of the plasma boundary. At the stochastic region, a shear of poloidal flow has been observed, while no shear of toroidal flow has been observed. The toroidal flow shear changes only in the nested magnetic flux surface region. A difference of density fluctuation property has been observed between co- and counter-flowing plasmas, where toroidal flow shears are formed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Numerical verification of Orbit and Nemato codes for magnetic topology diagnosis

We present the results of a benchmark study involving the Orbit and Nemato codes. The two codes have been used to compare magnetic structure in a reversed-field pinch (RFP), where conserved magnetic structures/islands appear both in the core (dominated by m = 1 modes) and in the edge (dominated by m = 0 modes). As input, a snapshot of a 3D nonlinear MHD visco-resistive simulation (produced by the SpeCyl code) has been used. The first test is given by the reconstruction via Poincaré surface of section plot of an island generated by a single mode. In this case, the magnetic field topology corresponds to a time-independent Hamiltonian and shows conserved flux-surfaces used as a reference. Both codes successfully yield field lines which follow the same flux surfaces, in both the m = 1 and m = 0 cases. The benchmark between the codes has then been extended to a more complex configuration with chaotic magnetic field, using as input a fully 3D multiple mode RFP condition, characterized by the typical chain of edge magnetic islands providing a transport barrier. Finally, a quantitative benchmark has been performed, using the same 3D input, by estimating the correlation length of the magnetic field line in a bounded stochastic domain. The conclusion is that both codes yield consistent Poincaré plot structure on one hand, and very good quantitative agreement in correlation length estimate. This gives confidence to the application of both codes to magnetic topology in the RFX-mod device, for which they are used routinely, as well as for a generic fusion device.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Stochastic-field cavitation model

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Stochastic and deterministic causes of streamer branching in liquid dielectrics

Streamer branching in liquid dielectrics is driven by stochastic and deterministic factors. The presence of stochastic causes of streamer branching such as inhomogeneities inherited from noisy initial states, impurities, or charge carrier density fluctuations is inevitable in any dielectric. A fully three-dimensional streamer model presented in this paper indicates that deterministic origins of branching are intrinsic attributes of streamers, which in some cases make the branching inevitable depending on shape and velocity of the volume charge at the streamer frontier. Specifically, any given inhomogeneous perturbation can result in streamer branching if the volume charge layer at the original streamer head is relatively thin and slow enough. Furthermore, discrete nature of electrons at the leading edge of an ionization front always guarantees the existence of a non-zero inhomogeneous perturbation ahead of the streamer head propagating even in perfectly homogeneous dielectric. Based on the modeling results for streamers propagating in a liquid dielectric, a gauge on the streamer head geometry is introduced that determines whether the branching occurs under particular inhomogeneous circumstances. Estimated number, diameter, and velocity of the born branches agree qualitatively with experimental images of the streamer branching.

36 MATERIALS SCIENCE↗

DOE OSTI2013

Simulation study of wave phenomena from the sheath region in single frequency capacitively coupled plasma discharges; field reversals and ion reflection

Capacitively coupled radio-frequency (RF) discharges have great significance for industrial applications. Collisionless electron heating in such discharges is important, and sometimes is the dominant mechanism. This heating is usually understood to originate in a stochastic interaction between electrons and the electric fields. However, other mechanisms may also be important. There is evidence of wave emission with a frequency near the electron plasma frequency, i.e., ω{sub pe}, from the sheath region in collisionless capacitive RF discharges. This is the result of a progressive breakdown of quasi-neutrality close to the electron sheath edge. These waves are damped in a few centimeters during their propagation from the sheath towards the bulk plasma. The damping occurs because of the Landau damping or some related mechanism. This research work reports that the emission of waves is associated with a field reversal during the expanding phase of the sheath. Trapping of electrons near to this field reversal region is observed. The amplitude of the wave increases with increasing RF current density amplitude J(tilde sign){sub 0} until some maximum is reached, beyond which the wave diminishes and a new regime appears. In this new regime, the density of the bulk plasma suddenly increases because of ion reflection, which occurs due to the presence of strong field reversal near sheath region. Our calculation shows that these waves are electron plasma waves. These phenomena occur under extreme conditions (i.e., higher J(tilde sign){sub 0} than in typical experiments) for sinusoidal current waveforms, but similar effects may occur with non-sinusoidal pulsed waveforms for conditions of experimental interest, because the rate of change of current is a relevant parameter. The effect of electron elastic collisions on plasma waves is also investigated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Nonlinear scattering term in the gyrokinetic Vlasov equation

Nonlinear scattering term is found from the nonlinear gyrokinetic equation by decoupling the perturbed gyrocenter motion from the unperturbed motion. The gyro-center distribution function is determined by the well-understood unperturbed motion, with the effects of fields perturbation included in the nonlinear scattering term, which explicitly reveals the nonlinear stochastic dissipation on the time scale longer than the wave correlation time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Shear avalanches in metallic glasses under nanoindentation: Deformation units and rate dependent strain burst cut-off

Indented metallic glasses at the nanoscale deform via strain bursts. Conventional continuum descriptions are not appropriate for such highly stochastic, intermittent deformations. In this study, after a statistical analysis of strain bursts in five metallic glasses, the dependence of the cut-off of the strain burst size on deformation units and loading rate is established. For soft metallic glasses with smaller deformation units, cut-off of the strain burst size truncates the scale-free behavior at larger strain burst sizes. For hard metallic glasses, scale-free behavior occurs in a wide range of strain burst sizes.

36 MATERIALS SCIENCE↗

DOE OSTI2013

Irradiation-induced composition patterns in binary solid solutions

A theoretical/computational model for the irradiation-driven compositional instabilities in binary solid solutions has been developed. The model is suitable for investigating the behavior of structural alloys and metallic nuclear fuels in a reactor environment as well as the response of alloy thin films to ion beam irradiation. The model is based on a set of reaction-diffusion equations for the dynamics of vacancies, interstitials, and lattice atoms under irradiation. The dynamics of these species includes the stochastic generation of defects by collision cascades as well as the defect reactions and diffusion. The atomic fluxes in this model are derived based on the transitions of lattice defects. The set of reaction-diffusion equations are stiff, hence a stiffly stable method, also known as the Gear method, has been used to numerically approximate the equations. For the Cu-Au alloy in the solid solution regime, the model results demonstrate the formation of compositional patterns under high-temperature particle irradiation, with Fourier space properties (Fourier spectrum, average wavelength, and wavevector) depending on the cascade damage characteristics, average composition, and irradiation temperature.

36 MATERIALS SCIENCE↗

DOE OSTI2013

Non-polynomial extensions of solvable potentials à la Abraham-Moses

Abraham-Moses transformations, besides Darboux transformations, are well-known procedures to generate extensions of solvable potentials in one-dimensional quantum mechanics. Here we present the explicit forms of infinitely many seed solutions for adding eigenstates at arbitrary real energy through the Abraham-Moses transformations for typical solvable potentials, e.g., the radial oscillator, the Darboux-Pöschl-Teller, and some others. These seed solutions are simple generalisations of the virtual state wavefunctions, which are obtained from the eigenfunctions by discrete symmetries of the potentials. The virtual state wavefunctions have been an essential ingredient for constructing multi-indexed Laguerre and Jacobi polynomials through multiple Darboux-Crum transformations. In contrast to the Darboux transformations, the virtual state wavefunctions generate non-polynomial extensions of solvable potentials through the Abraham-Moses transformations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

The effect of magnetic flutter on residual flow

The hypothesis that stochastic magnetic fields disrupt zonal flows associated with ion temperature gradient turbulence saturation is investigated analytically with a residual flow calculation in the presence of magnetic flutter. The calculation starts from the time-asymptotic zero-beta residual flow of Rosenbluth and Hinton [Phys. Rev. Lett. 80, 724 (1998)] with the sudden application of an externally imposed, fixed magnetic field perturbation. The short-time electron response from radial charge loss due to magnetic flutter is calculated from the appropriate gyrokinetic equation. The potential evolution has quadratic behavior, with a zero crossing at finite time. The crossing time and its parametric dependencies are compared with numerical results from a gyrokinetic simulation of residual flow in the presence of magnetic flutter. The numerical and analytical results are in good agreement and support the hypothesis that the high-beta runaway of numerical simulations is a result of the disabling of zonal flows by finite-beta charge losses associated with magnetic flutter.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Linewidth of the harmonics in a microwave frequency comb generated by focusing a mode-locked ultrafast laser on a tunneling junction

Previous analyses suggest that microwave frequency combs (MFCs) with harmonics having extremely narrow linewidths could be produced by photodetection with a mode-locked ultrafast laser. In the MFC generated by focusing a passively mode-locked ultrafast laser on a tunneling junction, 200 harmonics from 74.254 MHz to 14.85 GHz have reproducible measured linewidths approximating the 1 Hz resolution bandwidth (RBW) of the spectrum analyzer. However, in new measurements at a RBW of 0.1 Hz, the linewidths are distributed from 0.12 to 1.17 Hz. Measurements and analysis suggest that, because the laser is not stabilized, the stochastic drift in the pulse repetition rate is the cause for the distribution in measured linewidths. It appears that there are three cases in which the RBW is (1) greater than, (2) less than, or (3) comparable with the intrinsic linewidth. The measured spectra in the third class are stochastic and may show two or more peaks at a single harmonic.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Collective flow properties of intermediate mass fragments and isospin effects in fragmentation at Fermi energies

Within a microscopic transport model (Stochastic Mean Field) we analyze the collective flow properties associated to the intermediate mass fragments produced in nuclear fragmentation. We study the transverse and elliptic flow parameters for each rank in mass hierarchy. The results are plotted for {sup 124}Sn + {sup 124}Sn systems at an energy of 50AMeV and for an impact parameter b=4fm. The correlation with the dynamics of the isospin degree of freedom is also discussed and the results are presented for the same systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2013

Stochastic thermodynamics of fluctuating density fields: Non-equilibrium free energy differences under coarse-graining

We discuss the stochastic thermodynamics of systems that are described by a time-dependent density field, for example, simple liquids and colloidal suspensions. For a time-dependent change of external parameters, we show that the Jarzynski relation connecting work with the change of free energy holds if the time evolution of the density follows the Kawasaki-Dean equation. Specifically, we study the work distributions for the compression and expansion of a two-dimensional colloidal model suspension implementing a practical coarse-graining scheme of the microscopic particle positions. We demonstrate that even if coarse-grained dynamics and density functional do not match, the fluctuation relations for the work still hold albeit for a different, apparent, change of free energy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Test particle study of ion transport in drift type turbulence

Ion transport regimes in drift type turbulence are determined in the frame of a realistic model for the turbulence spectrum based on numerical simulations. The model includes the drift of the potential with the effective diamagnetic velocity, turbulence anisotropy, and dominant waves. The effects of the zonal flow modes are also analyzed. A semi-analytical method that is able to describe trajectory stochastic trapping or eddying is used for obtaining the transport coefficients as function of the parameters of the turbulence. Analytical approximations of the transport coefficients are derived from the results. They show the transition from Bohm to gyro-Bohm scaling as plasma size increases in very good agreement with the numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Open-loop control of noise amplification in a separated boundary layer flow

Linear optimal gains are computed for the subcritical two-dimensional separated boundary-layer flow past a bump. Very large optimal gain values are found, making it possible for small-amplitude noise to be strongly amplified and to destabilize the flow. The optimal forcing is located close to the summit of the bump, while the optimal response is the largest in the shear layer. The largest amplification occurs at frequencies corresponding to eigenvalues which first become unstable at higher Reynolds number. Nonlinear direct numerical simulations show that a low level of noise is indeed sufficient to trigger random flow unsteadiness, characterized here by large-scale vortex shedding. Next, a variational technique is used to compute efficiently the sensitivity of optimal gains to steady control (through source of momentum in the flow, or blowing/suction at the wall). A systematic analysis at several frequencies identifies the bump summit as the most sensitive region for control with wall actuation. Based on these results, a simple open-loop control strategy is designed, with steady wall suction at the bump summit. Linear calculations on controlled base flows confirm that optimal gains can be drastically reduced at all frequencies. Nonlinear direct numerical simulations also show that this control allows the flow to withstand a higher level of stochastic noise without becoming nonlinearly unstable, thereby postponing bypass transition. In the supercritical regime, sensitivity analysis of eigenvalues supports the choice of this control design. Full restabilization of the flow is obtained, as evidenced by direct numerical simulations and linear stability analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗